Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy

被引：135

作者：

Geng, Xianguo ^{[1
]}

Zhai, Yunyun ^{[1
]}

Dai, H. H. ^{[2
]}

机构：

[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China

[2] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2014年 / 263卷

基金：

中国国家自然科学基金;

关键词：

cmKdV hierarchy; Algebro-geometric solutions; Baker-Akhiezer function; Trigonal curve; TRIGONAL CURVES; ABELIAN FUNCTIONS; EQUATION; BOUSSINESQ; KDV; DECOMPOSITION; FLOWS;

D O I：

10.1016/j.aim.2014.06.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Based on the stationary zero-curvature equation and the Lenard recursion equations, we derive the coupled modified Korteweg-de Vries (cmKdV) hierarchy associated with a 3 x 3 matrix spectral problem. Resorting to. the Baker-Akhiezer function and the characteristic polynomial of Lax matrix for the cmKdV hierarchy, we introduce a trigonal curve with three infinite points and two algebraic functions carrying the data of the divisor. The asymptotic properties of the Baker-Akhiezer function and the two algebraic functions are studied near three infinite points on the trigonal curve. Algebro-geometric solutions of the cmKdV hierarchy are obtained in terms of the Riemann theta function. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：123 / 153

页数：31

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